Interquad capacity balancing of telephone cable circuits



March 18, 1930.

H. JORDAN'ET AL `1,751,333

piled Dec. 4, V1928 2 sheets-sheet 1 LL-[fu ,LLL 5TH L l L L l I.

INTERQUAD CAPACITY BALANCING OF TELEPHONE ACABLE CIRCUITS u [Il INvl-:N/ToRs Ems Janv/z/ ATToRNY INTERQUAD CAPACITY BALANCING OF TELEPHONE` CABLE CIRCUITS Filed Dec. 4, 1928 2 Sl'leets-Sheefl 2 MMM ATTORNEY i Patented Mar. #18, 1930 UNITED STATES PATENT OFFICE HANS JORDAN AND'ROBERT'GOILDSCIIIIYIID'J?, OF BERLIN-KARLSHORST, GERMANY,

ASSIGNORS TO GENERAL ELECTRIC COMPANY, A CORPORATION OF NEW YORK INTEBQUAD CAPACITY BALANCI'NG or rELErHoNE CABLE cmcUIrs Application led December 4, 1928, Serial No. 323,674, and in Germany December 22, 1927.

This invention pertains to capacity balancing between closely paralleling transmission circuits with the object of preventing current impulses transmitted over one such circuit from influencing the other circuit through the medium of capacitative couplings between such circuits. More specifically, the invention discloses a novel scheme applicable principally to quadded between the transmission circuits of a first and of a second quad in such 'manner that signals transmitted over the circuits of the one quad will produce no interfering effects upon the circuits of the second quad or vice versa.

The invention in essence consists in measuring the capacitative couplings between the speaking circuits of 'the irst and coupling values thus obtained, determining directly by means of a mathematical process the values of nine fixed capacitieswhich, when properly connected between suitable conductors of the one and of the other quad in accordance with the coupling equations will cause all the inter-quad couplings between the transmission circuits simultaneously to disappear so that the speaking circuits 3 of the one quad will produce no interfering ei'ects upon the speaking circuits of the other telephone cable for balancing the couplings those of the second quad and, from the has formerly been necessary in balancing up Inter-quad capacities to measure and correct the couphngs between certain speaking circuits before the coupling 4between other speaking circuits can'be measured and cor- 5l) rected. A third advantage ofthe scheme dis- -closed herein consists in the fact that, in

balancing up quadded cables on a large scale, a much smaller number of types and sizes of condensers need be kept in stock than was formerly the case.

It is the well known practice in manufacturing cables for use in long distance telephone service, to twist together the lead and return wire constituting each physical circuit. Two such twister pairs are in turn twisted into a quad to constitute the lead and return conductor of the phantom circuit in a phantom group. 4Each cable contains a number of such quads. The twisting is done in a scientific manner to reduce in so far as possible, the interfering effects between the various talking circuits of the cable which result from the inductive and capacitative couplings between the same. 'In spite of the precautions taken in this respect, however, there are residual unbalancenefects which in some instances become objectionable. The capacitative unbalances of short sections of cable 'can be offset by suitably connecting iXed capacities between certain conductors of the one and the other groups of speaking 'complete symmetry between quads, by makmg sixteen part capacities all equal or (2) by .balancing up the nine capacitative couplings between speaking circuits.

In respect to the second view above, vit is well known that the capacitative coupling i between two speaking circuits can be.balanced -by appropriate connection of a single condenser between a conducto-r of one speakingcircuit'and a suitable conductor of a second speaking circuit. It thus appears possible to remove the nine capacitative couplings between the s eaking circuits of a first anda second qua by the proper connection between certain conductors of the irst and second quad of only nine suitably chosen capacities. On the other hand, if the first method of balancing mentioned above is decided upon then fifteen condensers are required for balancing purposes, i. e., fifteen additions which make all' the smaller part capacities equal to the reatest.

ow, the present invention starts from the conce tion of removing the nine capacitative couplmgs bythe method of Vconnecting only nine condensers between the conductors of the'speaking'circuits. Prior to this invention, no method has been outlined for determining the values and mode of connection of 'i these nine balancing condensers in a practical case. A novel mathematical procedure has,

therefore, been worked out for determining directly from the nine measured capacitative couplings the values of the nine capacities required for balancing the same. This mathematical process, therefore, constitutes an essential part of the present invention.

Havingoutlinedmapreliminaryway above the problem involved, the balancing procedure will now be explained in detail with the aid of the drawings, in which Figure 1 shows schematically a pair of quads in a cable with the sixteen part capacities between the conductors of the one and of the other quad indicated. Fig. 2 shows a diagram of two speaking circuits with the part capacities between the conductors of the one and the other indicated. Fig. 3 shows the quads of-Fig. 1 with the part capacities()1 to C16 not shown, and with certain balancing capacities indicated. Fig. 4 shows a chart used in mathematical determination of thel balancing capacities. Fig. 5 gives a chart in which a numerical example illustrating the determination of the balanced up, using the last met balancing capacities in .a worked out.

In Fig. 1conductors l1, 2, 3 and 4 constitute one quad of the cable while conductors 5, 6, 7 and 8 constitute apsecond quadltherein. In the first quad, the side circuits are indicated byA1 and A2, respectively, while the phantom is indicated by A. In the second uad, the corresponding designations are B1,

2 and B. The capacities C1 t0 C16, inclusive, show all possible part capacities between the tors of thesecond quad. By connecting in parallel with each part capacity C a fixed capacity X such that U1'I'lX1=02+X2 013+X13, the inter-quad couplings between the speaking circuits will `be balanced up so that circuits A, A1 and A2 will have no reaction on B, B1 and B2 or vice versa.

T he truth of the above statement can be demonstrated by reference to Fig. 2in which conductors AB represent one speaking circuit and conductors CD the second. The inherent part capacities between the conductors of one and the other speaking circuits are inspeciiic case is conductorsof the first quad and the conducdicated by n1 to n.1, respectively. If a voltage is impressed between conductors CD, in or-l der that no effect be produced on circuit AB as a result thereof, it is necessary that the following relation exist betweenthe part capacities:

l 'l' .n2-n4 In other werds, under the assumption of Equation (2), the arrangement constitutes a balanced bridge of which the capacities r1/1 t0 n1, inclusive, are the balancing arms and conductors AB the equipotential points.

If the relation between the part capacities -is not such as to furnish the equality repre-` sented by Equation (2)- then a balance can v be obtained by connecting in parallel .with each part capacity n a fixed capacity az, such that j n1+1=n2'|2=n3|3=n1+1. (3)

Under the conditions of Equation (3), the bridge, of course, becomes balanced, since all the balancing arms contain a like impedance. It'is not necessary, however, to usev four caacities for balancing up the bridge. Re-

erring to Equation (2), if the ratio on the left side of the equation does not equal that on the right, it can be ina-de the same by connecting in shunt with one of the capacities fn, a single capacity :t of proper value to reduce the equation to an equality.

Thus, referring now to Fig. 3 which shows sections of. the uads A and B of Fig. 1, with the capacities 1 to C16 not indicated, each side circuit to side circuit cou ling can be libd discussed above, by connectmg onl'y a single condenser `between a conductor of one and v quired in or same manner, f in to phantom couplings, each circle A to D repthe other side circuit. As an illustration of this, Fig. 3 shows the balancing ofthe coupling between side circuits A1 and B1 by means of the single capacity t1. The other side'to side couplings AIBZ, A2B1 and AzBz .can correspondingly be balanced up by suitably 'connecting a single condenser in each case.

In vbalancing u the side circuitto phantom circuit coup ings by this procedure, it should be remembered, of course, referring to Fig. 2, that if AB represents the side circuit and CD the phantom, then circles C and D each represent the two conductors constituting the lead and return path of the phantom circuit and the capacities al to m,

inclusive, each re resent the two part capacities from acon uctor of the side circuit to the two conductors comprising the lead or return path of the tphantom circuit. Iny the etermining the phantom resents the two conductors constituting the.

leader return path of a phantom circuit and each capacity n is the sum of the four-part capacities between such pairs of conductors.

In balancing up a side to phantom coupling, two additional capacities are, required in order not to disturb the previ'osly.bal'-V anced side to side circuit couplings. The manner of connecting these two condensers is indicated in Fig. 3b by condensers t2 to t8 which balance the side to phantom coupling A1B. There are three other side to phantom couplings which require balancing by the same proce-dure, namely, AQB, B1A and BZA. In order to balance up the phantom to phantom couplin AB, four capacities are reer not to disturb the previously balanced side to side and side to phantom couplings. In Fig. 3C, condensers ti to t7 indicate the mode of connecting the balancing capacities for this case. The method outlined immediately above desciibesthe` known procedure for balancing up the inter-quad capacitative couplings. It will be seen that the method requires a total of sixteen capacities. The method is cumbersome inrfthat the side to side couplings must be measuredand corrected before measurements can be made Aon the side to phantom couplings, since the balancing up of the former effects the latter. Similarly, the side to phantom couplings must be measured and corrected before the .phantom to phantom coupling can be attacked. It is thus apparent that the known Y i f method of balancing the couplings is not only long and tedious but requires the mainmumnumber of balancing capacities. Furthermore, where such procedure isfollowedl on a large scale, it re uires maintaining in stock a supply of con in groups of one, two and four units each for balancing the side to side, side to phantom andphantom to phantom couplings, respectively. With the method of the pi'esent disclosure, however, it would be requiredito maintain in stock only the-single unit ele-- ments.

Coming, now, to a discussion of the present disclosure and referring to Fig. 2, the `capacitative coupling between the circuits AB and CD `may be calculated according to the following equation:

comparison with the average value. v"lhe ensers manufactured nsl deviation of the capacities fn, from the average value isvsmallv in v equation itself is derivable from a consideral tionof thebalanced bridge arrangement ofk the capacities n, to .m, inclusive. `Now, in'

order that the coupling .capacity le of Equation (4) disappear, the inherent part capacities should each receive an addition such that .7c becomes zero, 1. e.,

In other words the equation for theaddtions hasthe same form as that for the part capacities n but with the sign of 7c reversed.

The general Equation (6) vcan be applied to the nine couplings between the speaking circuits of quads A and B of Fig.l l, reinem'- bering, of course, that wherever a phantom circuit is involved, two or four part capacities must replace certain of the single capacities of Equation (6). Keeping this point in the nine couplings between thev speaking cir -f cuits of Fig. 1 must comply with the follow Table I Circuit Equacoupling tion i mind, the additions required for removing" The values w1 to m16, inclusive, are the additions to part capacities C1 to C16, respectively, of Fig. 1 required for removing the couplings.'

It will be noted that the group of equations in Table I comprise sixteen unknown quantiv ties with 'only nine equations `for evaluating the same. The problem, therefore, cannot be solved uniquely. Arbitrary 'values can be assigned to any seven of the variables and the equations solved uniquely for the remaining lnine roots. Practically, of course, seven of vthe variables would be set equal to zero, since physically this would correspond to omitting the connection of balancing condensers between the corresponding conductors. Now, there are 1607F-11,440 different combinations of the variables af.' having seven lgiven set' of measured coupling values, which of the above combinations will produce nine positive roots in addition to the seven zero values. This isdue to the fact that whether roots work out positive or negative depends upon the sign of the measured couplingl values and also upon their relative magnitudes. Now, there are something like 2X 108 different ways of arranging the values k, ac-y cording to their relative magnitudes also taking into account the possible. sign combi-- nations. Since any given measured set of coupling values might b'e any one of these possible arrangements, it is readlly apprehended thatit is almost impossible to predict what combinations of `seven values of the variables set equal to zero will produce ynlne positive y roots in a given case.

For a given set of measured coupling values, one might, of course, proceed to select at random successive combinations of seven variables set equal to zero and solve the equations simultaneouslyfor the remaining nine, until by chance, a combination was found producing nine positive roots. The

Work involved in such procedure, however,-

would soon become prohibitive if the first few guesses were wrong.

It, therefore, becomes necessary to devise some fairly simple method whereby a solution may be obtained in a given case producing nine positive and seven zero roots. Such a method constitutes an essential part of thel present invention and consists in assuming suitable solutions for the nine equations of Table I individually, combining these solutions for the individual equations in such manner as t obtain a general solution for all nine 'of lthe equations, and then applying to the general solution certain alterations which are ineffective as to the individual equations, until seven values are reduced to zero Vand leaving nine positive values.

rThe equations of Table I are s et forth in a somewhat different form on the chart of Fig. 4. Since the signs of the variables to wm is the important feature. here, the variable designations m1 to wm are placed in the upper row of squares on the chart. In the squares below the ws are placed the signs thereof, in accordance with their occurrence in Equaequation designation is indicated in column 1 while column 2 indicates the circuit coupling designation and column 3 gives the coupling constant 7c. It is important to point out atv this point that in measuring the coupling lc, between any'two speaking circuits, the measured value 7c may be plus or minus and that in Equations (a) to (i) inclusive,

minus the measured value of c including its sign, is taken.

Referring now to Fig. 4, assume a solution for Equation' (a) by apportioning the measured value of the coupling constant equally among the variables of opposite sign thereto, the remaining variables, for the moment, being assumed zero. Thus, for example, if the measured value k1 is positive, the sfolution of Equation (a) is assumed in the orm with w1 to :1:4 and w13 to m18 taken as zero. If, now, the values of the variables assumed for the solution of Equation (a) are substituted in Equations (o) to (i) inclusive, respectively, it will be noted that in each case they produce zero resultant effect on such equations, owing to the sequence of the signs 'of the variables in such equations. For example, if

the value -gl be substituted in Equation (b) for the variables m5 to m15, the effect will be zero, since m5 and we are negative, while and wg are positlve. The` values :1f/'9 to w12,-

of course, do no t affect Equation (b), since theyare not present therein. The same result would be obtainedby applying the assumed solution of Equation (a) to any of the Equations (b) to (i), inclusive. Thus the assumed solution, while valid for Equation (a), has `zero resultant eiect upon Equations (b) to (i) inclusive. The same result would follow had the measured value of cl been negaive, requiring the assignment of the value .8 I toa/116, inclusive, of Equation (a) in order to establish an equality.

to the positive variables :v1 to wi and m18 so tions (a) to (z'), inclusive, of Table I. The

Havin assumed the solution for Equation p measured value of k2 is positive and, consel posite sign thereto.

quently, apportion k2 equally among the negatlve values of m in Equation (b), giving The' other variables :v of Equation (Z) are,

vfor the moment, assumed equal'to zero. e The assumed solution for Equation (b) it will be noted from an inspection of the signs of Fig. 4, has zero resultant eect upon the remaining Equations (a) and (o) to (i), inclusive.

Thus, inserting the value for the variables ma to ma in Equation (a), it will be seen that the total eect is Zero, since ma and ,mi are positive while m5 and 006 are negative in such equation. A similar result will likewise be obtained for Equations (c) to inclusive. Also, if the measured value of k2 were negative instead of positive the same result would follow by assigning the value yg to the vari-v ables w1, m2, m7, and w8.

Thus, individual. solutions Vhave been obtained for Equations (a) and (b) which liave no reactive' effect upon the remaining equations. In asimilar manner a solution for Equation (c) yis assumed by'assigning the value 1%* to the variables of opposite sign thereto in such equation, and likewise, in Equation (d) -a-solution is obtained by assigning the value Iii to the variables of opposite sign thereto, and in Equation (e) as# signing the value to the variables of op- Coming now to Equation (f), if a value l@ is assigned to the variables of opposite sign, an inspection of Fig. 4 will show that the solution thus assumed, while producing zero resultant effect upon Equations (b) to (e) and (g) to (i), inclusive, will produce a coupling elitect when the values are substi-4 tuted in Equation (a). For example, if the measured value la@ is negative, the value @2g is assigned to the variables m1 and m4 in Equation (f) Substituting these values in Equation (a) gives a total resultant eeet equal to Ica, since both m1 and'. aai are. positive in Equation (a). In order, therefore, to oilset the effect of the assumed solution for ae, inclusive. For negative lo, the value Equation (f) on Equation (a), in addition to assigning the value 4 is also assigned toA the variables m5 to w8, inclusive, or to the variables m9 to w12. Thus, for example, with the .measured value of cnegative, the value t2? is assigned to the variables :v1 and w, and

the value isiassigned to the variables :v5

to aeginclusive,l for enample, by placing such values in the proper squares of a chart similar to Fig. 4. If these values of the variables are substituted in Equation (a), the total re'- sulta'nt effect will be zero, since 1+4= -l-c, v

@f to the variablesen to w8, inclusive, has no eect on the solution of Equation (7") since these variablesl do not appear in that equation. Had the The assignment of the value measured value 7c@ been positive, the solution of Equation; (f) would be obtained by assigning the value to the variables m2 and w3 and the value positive la7/by assigningk? to :v6 and m7 and in. addition assigning to w1 to um, or' :i119 to is assigned to m5 and w8 and the value t0 the variables, w1 to m4, or aim to w16, inclusive,

(a) in addition uw: value 4 the variables :v1 to mi or w13 to m16, inclusive.

Fox/'Equation (i), the value 2? is assigned to the variables of opposite sign, and to o'set.

the coupling eii'ect on Equation (a) the value 4 is assigned to m5 to w' or m9 to w12, inclusive.

to the variables m5 to wg,

lll

is assigned to Suppose, now, that the Values assigned to the variablesin'the solution of the individual equations were inserted inthe proper squares of a chart Vsimilar to Fig. 4 and the columns stituting a single value foreach variable m,

added vertically. Thus, certain squares lin Equation (a) would contain `the value 1 and in Equation (b) certain 'squares would contain thev value i, etc. The columns w1 to w16', inclusive, when summed up yelically, would thus give a set of resultant values conand set of resultant values would have the peculiar property that it would satisfy all of the Equations (a) to (i), inclusive. That this must be the case follows from the manner in which the resultant set of values Was obtained, i. e., by Vsumming up nine Sets of individual values each of which constituted a solution of one of the Equations (a) to (i) inclusive, but which had zero resultant effect on all of the other equations- The set of values obtained in this manner constituting a lgeneral solution for the nine coupling equations, will, owing to the manner in which it was obtained, as a general rule, comprise sixteen positive values. Thus far, therefore. it is not a solution of the type desired since, as Was explained above, the desired solution must contain nine positive roots and seven zero roots. The next problem, therefore, is to alter the general solution in such manner that seven of the variables will be reduced to zero, leaving only nine positive values. This alteration must be accomplished in such manner that the general solution finally obtained Will individually satisfy all of the nine Equations (a) to inclusive.

Now, it can be shown, with the aid of Fig. 4, that certain order changes may be applied to the general solution Without affecting its validity as a solution of the nine equations. For example, the values of the variables m1 to m8,' inclusive, in the general solution, might be simultaneously altered by the same amount without affecting the validity of the general solution. This is due to the fact that. owing to the arrangement of the signs of the variables m1 to m8, inclusive, in the nine equations, the same change applied to all such variables would add up to zeroi each equation. Thus, if the value p were added to these variables, the effect on Equation (a) would be 4-4p=0, since w1 toa/:4 are positive While m5 to ma are negative. Similarly, 1n Equatlon (b), m1, m2, m7 and m8 are positive While ma to ai@ are negative, and so on for all the remaining equations.

Having thus demonstrated hou7 one alteration may be applied to the general solution without affecting its validity as a solution of the nine equations, a table will now be included showing the possible changes lof this type. Without affecting the coupling equations, the following variables may be simultaneously increased or diminished by the same amount.

Table II (a Values 1 to 4 in Groups I to IV 1 Values 1 to 4 in Groups I and II 62 Values 1 to 4 in Groups I and III b3 Values 1 to 4 in Groups? III and IV fb., Values 1 to 4 in Groups II and IV (c1). Values 1 and 2 in Groups I and II (c2) Values 3 and 4 in Groups I and II (c3) Values 1 and 2 in Groups III and lIV .(04) Values 3 and 4 in Groups III and IV (c5) Values 1 and 3 in Groups I and III (ou) Values 2 and 4 in Groups I and III (c7), Values 1 and 3 in Groups II and IV (08) Values 2 and 4 in Groups II and IV simultaneously by the same amount.

By properly appl ying'certain of the alterations specified in Table II to the general s0- lution, it is possible to successively reduce certain of the variables to zero. This process is continued until finally seven such values are so reduced, leaving only nine positive roots. The procedure, of course, is to apply an alteration in accordance With Table I, which will first reduce the smallest root in the general solution to zero. Thus, suppose the smallest root is $14261. This root could be reduced to zero Without affecting the validity of the general solution by adding -d to the general solution in accordance with the alterations a, b3, b4, c3 or e8 of Table II, Whichever such alterations seem best adapted in the particular case. Having thus reduced the smallest root to zero in this manner,

vthe smallest of the values remaining after such alteration is next reduced to zero in a similar manner, and so on.

In applying the method outlined above to specific problems it has been found that in some instances it is difficult to reduce as many as seven of the variables to zero owing to the restrictions as to the types of alterations Which can be applied in accordance with Table II. For this reason a slight modification of the method described above will now be outlined by means of which latter method itis always possible to reduce seven of the variables to zero, leaving nine positive values. This latter method will be illustrated with a numerical example, Which will also furnish a definite picture as to the manner in which the general process is applied.

Referring again to Fig. 4, it Was demon.

strated above that in general the apportionmentof a given coupling constant equally among the variables of opposite sign thereto constitutes a solution for the corresponding coupling equation but Which is ineffective as applied to the other equation. Now, it isnot necessary to apportion the coupling constant equally among all the variables of opposite ,sign to accomplish this result. For example, referring to Fig. 4, assume a Asolution for Equation (a) by assigning .the value tion the assumed solution Will be {c2-2 apportioned equally among the variables of op- .variablesof opposite sign in Group'II and posit-e sign thereto in Group I only. Such a solution, While producing zero effect on Equations (c) to (i), inclusive, Will produce a coupling effect on Equation (a) since the variables m1 to all have the same sign in such equation. To offset the effect on Equation (a), therefore, in addition to assigning' thef'g i value to the-variables in Group I of opthe variables m5 to ma, inclusive, of Group II. In Equation (o), theassumed solution is in Group III and to offset the coupling ef-l +3 is also feCt on Equation (a) the value 4 apportioned among `the variables' :r1 to :1f/'4,A

2 to the variables of opposite sign in Group I 4 inclusive, in Group II. In Equation (e),

inclusive. In-Equation (d), is assigned and in addition to the variables :1:5 to m8,

(If),` the solution is 56 bles of opposite sign in Group I and-[19 to assigned to the vvariathe variables :c5 to m8 in Group- II. In Equa# tion (g), the solution is 2 assigned to the lc i' to a', to an, inclusive, 1n Group I. In Equai tion (70,7% isffifsisigned to the variables of assigned to the variables of opposite sign is assigned to the variables opposite sign in Group III and to the u valuables/a1 to m4, mclusive, 1n Group I. In

.Equation (i), I? to the variables of opposite .out by the numerical example, lies in the fact that, irrespective of the signs of the measured coupling constants c, at least three of the variables Will be initially zero in the general solution, thus requiring the reduction to zero of only four variables by the methods outlined above.

Referring n ow to Fig. 5, which shows the application of the latter method to a specific example, column 1 of the chart shows the coupling designations in accordance with Fig. 1. Column 2' gives the coupling designations, as icl, 102, etc. Column` 3 gives the. -measured coupling valuesy 1n an actual case,

together With the sign thereof. Thus, the measured coupling constant k1 Was +100, k2 +80, etc. The upper portion of the squares in column 3 are marked negative and thel lower portion positive, andthe measured coupling value is in each case Written in opposite its proper sign. In Groups I to IV, inclusive the shaded portions under the variables w1 to m16 block out the s of the samesign as the measured coupling value, since the coupling value is never apportioned among such variables. For example, referring to the coupling A/B. the measured coupling is +100, and since the variables m1 to are positive the lower portions of the squares are blocked out, preventing the apportionment of the coupllng among such variables, While the lower l portion of the squares corresponding to m5 to m8, inclusive, are leftfree, permitting the apportionment of the coupling constant among them since the signs of these variables are negative.

For the coupling A/B the is assigned'to the variables :v5 to m8 since the measured value of k1 is positive. It might be Well to refer to the chart of Fig. 4 in connecvalue 1% =25.

l@ sign in Group IV and l? to the variableszaav tion With the signs of the' variables here.

For the coupling Al/B the value ,22 =40 is `assigned to the variables ac3 and w, since c2 is positive, and to offset thecoupling effect on Equation (a) the value the variables :v5 to we, inclusive. In the same manner, following down the entire seriesf values, the measured coupling value is apportioned equally among the variables of opposite sign in accordance with'the rules outlined above, and to prevent a coupling effect on Equation (a) an additional apportionment of E is assigned to' all the variables of Group I or Group II, asv the case may be, to

vshow that, irrespective of the signs of the measured coupling constants, three of the roots in Groups III and IV will always be initially zero in the general solution.

The final step in the solution consists in altering the general solution of line T in such manner as to'reduce four additional roots to zero. The necessary alterations, of course,

value 'in Group III so that w9=w1o or 11=12,'

as the case may be. Thus, in the example given, apply the alteration c6 of Table II by adding the Value +2 to m2, m4, m10 and w12. The code designation of the alteration applied is indicated in column 3 of Fig. 5 under T. The upper portion of ce shows the alteration applied while the lower portion of c6 shows the value of the variable altered after such modication. Thus, in the example, after modification 12=m11=2.

2. Next, apply the alteration c3 or 04 of Table II so that the smaller of the values m11 and :12,2 or and w10, as the case may be, by addition becomes equal to the other two values already equal, or vice versa. In case the two equal values are the smallest in Group III these two smallest Values are made equal to the smaller value of the remaining two values in the group. Thus, in the example, line c6, mu and m12 are now equal to 2, which is smaller than either 9=20 or w10=24. Consequently,

apply the alteration e., of Table II by adding the value +18' to the variables w11, 00,2, m1 and ail. This alteration, line c4 of Fig. 5, makes w=11=12=20, as shown.

3. Applythe alterations c, or c'8 so that the smallest number in Group IV becomes equal =2O is assigned to to zero. In the example, the smallest number in Group IV is m1=14. Hence, applying the alteration c1, add -14 to m5, w1, w13 and m15. Thisreduces m1 to zero, see line c7, Fig. 5.

4. Apply the alteration b2 of Table II so that the three equal values in Group III become zero. Hence, in the example, line b2 Fig. 5, add -20 to the variables w1 to m4, inclusive, and m0 to w12, inclusive, thus reducing m9, mi, and w12 to zero.

5. Apply the alteration b1 of Table II so that the, smallest value of Groups I and II become zero. Thus, in the example, w2=32 is now the smallest value in Groups I and II. Hence, line b1, Fig. 5, add -32 to m1 to w8, inclusive, in accordance with alteration b1, Table II, thus reducing m2 to zero.

6. Apply the alteration c1 or c2 so that the smallest remaining value in Groups I and II becomes zero. Thus, in the example, apply the alteration c2, Table II, by adding -22 to ma., m4, and thus reducing x4 to zero, line c2, Fig. 5.

Thebottom line of c2, Fig. 5, now gives the solution required consisting of nine positive values and seven zero values of4 the variables az, to wie, inclusive. This set of Values satisies all the nine Equations (a) to (i), inclusive, and hence if the capacities w1 to w18 of line c2, Fig. 5, are connected in parallel with the corresponding quad capacities c1 to 0,6, respectively, of Fig. 1, the couplings k1 to kg will be completely'balanced so that the talk-4 ing circuits at quad A will have no interfering eii'ect on those at quad B, or vice versa.

The final solution of line 02, Fig. '5, is, of course, but one-oi:l many possible solutions. For example, starting with the Values of line T, a different set'ofvariables might have been reduced to zero by the general methods outlined. Or initially, the values of k might have been apportioned as much as possible among Groups III and IV, or I and III, or II and IV, instead of between Groups I and II, as was done in the example shown., According to the particular groups thus stressed ldifferent final solutions would be obtained.

Solutions of the problem are not included herein showing the exact procedure when the l coupling apportionments are limited to the group pairs other than Groups I and II for the reason that the solution illustrated, shows suiciently well the general line of attack.

In dealing with long cable circuits, it may be necessary to balance up the inter-quad couplings at a number of points. For example, in loaded cable circuits, it might be advisable to balance the inter-quad couplings in each loading section.

tion employed in regular succession from balancing point to balancing point, in order that the nine balancing capacities will not be con- In suchl case, it is 1- recommended to change the scheme of soluat the first balancing point consists in limiting the coupling apportionments to Groups I and II,-then at the second point, the coupling apportionments should 'be limited to' groups say II and IV, and at the next point,- to Groups I and III, and so 0in-using all the combinations over and over again in regular succession.

In the claims: The capacities :v1 to mm' of Eqluations (a) -to (i) inclusive of Table I, wi l be referred to as the balancing capacities which in fact they are.' The phantom to phantom circuit coupling E uation (a) of able I will, for the sake of revity, be referred to by the term phantom equation. Likewise, the phantom circuit to side circuit coupling Equations (b) to (e) inclusive of Table I will be termed the phantom-side equations, while'the term side circuit equations will be utilized to desi ate the side circuit to side circuit` coupling quations (f) to (i) inclusive. By successive balancing capacities will be meant the ,values w1, m2 etc., occurring in the order shown by the equa'- tions of Table I above.

What we claim as new and desire to secure by Letters Patent of the United States is:

1. Method for balancing the couplings between adj acont-quads, especially in telephone cables, which consists in measuring the interquad couplings between the transmission circuits of the one and of the other quad, calculating from such measured couplings directly the values of the nine capacities for balancing the same, suitably connecting between the conductorsof the one and of the other quad, nine such capacities .whereby the inter-quad couplings are simultaneously made to disf' appear.

2. Method for balancing the couplings between ad'acent quads, especially in telephone cables, vvv ich consists in measuring the interquad couplings between the transmission circuits of the one and of the other quad, apportioning the measured couplings values vequal- Ily among the balancing capacities of opposite sign thereto in their respective coupling equations, rendering such apportionments in the side circuit equations ineiective asapplied to the phantom equation by further apportioning the couplings in the respective side circuit equations equally among four successive capacities of proper sign not occurring therein, summing up the values thus assigned the respective balancingl capacities, successively altering through c anges ineffective as to the individual equations thel set of resultant sums through like changes simul# taneously applied to certain groups thereof, until finally seven of the sixteen possible sums are'reduced to zero while the remaining nine assume positive values, pro erly 'connecting between `'the conductors o the one andl of'theother quad nine capacities corresponding'to said nine ,positive values,

whereby all the aforesaid interuad coplings are simultaneously made to 'sappeal".

v3. tween adjacent quads,fespecially intelephone cables, which consists in measuring the lnter- Method -for balancing the couplings bequady couplings. between the transmission circuits of the one and of the other quad, apportioning the measured couplings equally among the balancing capacities of opposite sign thereto4 Iin their respective coupling. equations, limiting such apportionment in a vance except for the equations having no f capacities therein, to two groups of four successive capacities, each -said group having i opposite dering s equations ineffective as applied to the phansi s in the phantom equation, rend apportionments in the other tom equation by further apportioning the y couplings in such other equations equally among the capacities in one group aforesaid of proper sign, summing up the values thus assigned the respective balancing capacities, successively altering'through changes ineffective as to the individual equations the set other quad, ninecapacities corresponding to said n1ne positive values whereby'- all the intersquad couplings aforesaid are simulta' neously made to disappear.

4., Method for balancing the couplings be tween adjacent quads, especially in telephone cable, which consists in-measuring the interyquad couplings between the transmission circuits of the one and of the otherquad, apportioning the measured couplings equally among the balancing capacities of opposite sign thereto in their respective coupling equations, limiting suchv apportionment inl advance except for the equations having no capacities therein, to two groups of f'our successivev capacities each, havin opposlte signs in the phantom equation, ren ering such apportionments in the other equations ineffective as applied to the phantom equation by further apportioning` the couplings in such other equation equally among the capacities in one group aforesaid of proper sign, summing up the values thusl assigned the respective balancing capacities, successively alter-l ing through changes ineffective as to the individual equations the set of resultant sums through like changes simultaneously applied to certain groups thereof, until at first iive sums in the two non-limited groups and finally two additional sums in the aforesaid limited groups are reduced to zero while the remaining nine of the sixteen between the conductors .of the onev and the other quad, nine capacities corresponding `to ossible sums Aassume positive values, proper y connecting saidl nine positive values whereby all the aforesaid inter-quad couplings are simultaneously made to disappear.

5. Method for balancing at a plurality of successive balancin points the-couplings between adjacent qua s, especially in telephone cables, which consists for each balancing point, in. measuring the inter-quad couplings between the transmission circuits of the one and of the other quad, apportioning the measured couplings equally among the balancing capacities of proper sign in their re- .spective coupling equations, limiting such apportionment in advance where possible, to

' signs in the phantom equation,.ren ering such two groups of four successive balancing ca-l l pacities, each said group havin opposite apportionments in the other` equations ineffective as applied to the phantom equation by further apportioning the couplings therein eually among the capacities in one group a oresaid of proper signfsummingup the values thus assigned the res ective balancin capacities, successively a terin throug changes inei'ectiveas to the individual equations the set of resultant sums, until sevenof the possible sixteen are reduced to zero while the remaining nine assume positive values, properly connecting between the conductors ofthe one and of the other quad at the balancing point in question, nine capacities corre-v sponding to said nine positive values whereby the inter-quad couplings at such balancing point are simultaneously made to disappear, changin `preferably in regular succession from ba ancing point to balancing point the combination of two groups aforesaid to which the apportioned values are limited.

In witness whereof, we have hereunto set Aour hands this 15th day of November? 1928.

HANS JORDAN. ROBERT GOLDSCHMIDT. 

